Herein is described an invented device for the educational purpose of demonstrating various operations with nonstandard counting procedures, mainly extending binary and other types of sequences by an additional digit or symbol to remain consistent with hereditary properties residing in the original or challenge sequence.
My methods and embodiments for extending sequences with deep hereditary structure have evolved from studies with continuous systems and generalized for discrete behavior.
For particularized versions of the original conceptual experiments, see my "Application of a Block-Wiener Mapping to a Homeostatic Learning System," Journal of Cybernetics 1971, 1,3, pp64-78. For sequences with interesting hereditary properties, see Sir Karl Popper's book: The Logic of Scientific Discovery, wherein lie many examples.